Computer and Machine Vision

Transcription

1 Computer and Machine Vision Lecture Week 5 Part-1 February 13, 2014 Sam Siewert

2 Outline of Week 5 Background on 2D and 3D Geometric Transformations Chapter 2 of CV Fundamentals of 2D Image Transformations and Convolutions (CV Chapters 3 & 4) Introduction to More Advanced 2D Transformations Bottom Up C without OpenCV Simple 2D Center-of-Mass Tracking Introduction to 2D Pattern Matching Next Time Sam Siewert 2

3 Backgrounder 2D and 3D Geometric Math Overview (Chapter 2 CV) Sam Siewert 3

4 Understand Geometric Transform Types Figure 2.4 2D Planar Transformations Sam Siewert 4

5 Primitive 2D Transformation Properties Sam Siewert 5

6 Primitive 3D Transformation Properties Sam Siewert 6

7 Translation and Rotation Studied in Physics (and Linear Systems) Vectors, Rotation Matrices 2D & 3D Simple C++ Starter vectmat.zip Ground-up OpenCV Tutorial Sam Siewert 7

8 OpenCV Linear Algebra Sam Siewert 8

9 OpenCV Linear Algebra Sam Siewert 9

10 Based on Studies of Perspective by Artists and Physics of Light Painted/Traced Edge Silk Screen Illumination Observer Viewpoint Rays Sam Siewert 10

11 Parallel Projection Cartography Orthographic Mercator (Cylindrical) Orthographic Sam Siewert 11

12 Vanishing Point Linear Perspective (1 to 3 Vanishing Points) Curvilinear (4 or 5 Vanishing Points) Single Vanishing Point Double Vanishing Point Sam Siewert 12

13 Perspective Concept Object Render Plane Intersections viewpoint Sam Siewert 13

14 Perspective Projection Normal Projection Used in Ray Tracing Define Extents of Render Plane l=left, r=right, t=top, b=bottom Viewpoint e is shown on Render Plane Move e out of Plane to Location of Camera/Viewer Fundamentals of Computer Graphics, 3 rd Edition - page 75 Sam Siewert 14

15 2D Image Transformations Basic PSF Convolutions Sam Siewert 15

16 Pixel Neighborhood Convention {P} Originally Sampled Frame or Sub-frame of Pixels {Q} First Transformation of {P} Negative Image {Q}=Saturation {P} Where Saturation for 8-bit Gray-level is 255 P4 P3 P2 P5 P0 P1 P6 P7 P8 Difference Image {R} = {Q} {P} is the time of sample of {Q} is greater than {P} A threshold (Part 2) From Histogram P0 is the Pixel of Interest in a Neighborhood So, for all pixels in {P}, if Q0=P1, then {Q} is the same image shifted one pixel to the left If {Q}={P}+beta, modifies brightness If {Q}={P} x gamma, modifies contrast If {Q}={P} x gamma + beta, modifies both contrast and brightness This Can Define a PSF for an Image Convolution e.g. Sharpen Sam Siewert 16

17 Common PSF Convolution See For all pixels, do {Q0 = P0*h0+P1*h1+P2*h2+P3*h3+P4*h4+P5*h5+P6*h6+P7*h7+P8*h8; } Convolution of image causes no change to Chapter 24 Sam Siewert 17

18 Median Filter Concept For all Pixels in Image do minpixel = min(p1, P2, P3, P4, P5, P6, P7, P8) maxpixel = max(p1, P2, P3, P4, P5, P6, P7, P8) If(P0 < minpixel) Q0 = minpixel Else If (P0 > maxpixel) Q0 = maxpixel Else Q0 = P0 Sam Siewert 18

19 Standard Median Filter Algorithm // zero histogram for for (i=0; i<=255; i++) hist[i]=0; for all pixels in Image P do { // All pixels in the kernel note value for (m=0; m<=8; m++) hist[p[m]]++; i=0; sum=0; while (sum < 5) { sum = sum + hist[i]; i = i + 1; } Q0 = i 1; Q4 Q3 Q2 Q5 Q0 Q1 Q6 Q7 Q8 } for(m=0; m<=8; m++) hist[p[m]]=0; Sam Siewert 19

20 Median Filter Algorithm Nearest Neighbor (p ) The Median Filter Uses Binning in range of 0 to Saturation of PGM (0 to 255) Obviates need to Sort the Value of Neighbors in Kernel 3x3 Q0 is the 5 th largest neighbor in the Kernel Must Zero Histogram of size 256 for Each Pixel Loop through all neighbors and bin them Each P[m] neighbor s value is the index into the histogram of counts for pixels at that value This filter provides noise suppression, but softens edges Truncated Median Filter Removes Noise and Sharpens Sam Siewert 20